Learn English – How and when did ‘impossible’ become a noun (as in ‘To achieve the impossible’)

Impossible itself never become a noun. This is actually a common construct where "the + adj" is used as a noun.

EDIT: As RaceYouAnytime pointed out, impossible was used as a noun in the past. But to the example sentence provided, "impossible" is not a separate noun, but "the impossible" is a construct where an adjective can be used as a noun, properly called a nominalized adjective.

He did the unforgivable.

She achieved the impossible.

But it can also be used to describe people. Examples include:

The deceased is survived by his wife.

The blind use assistive technologies.

He's only trying to help the rich. He doesn't care about the poor.

As explained in the answer to this question, these instances either involve omitting the real noun (ellipsis), or referring to people by their attributes (metonymy).

Let's look at these sentences again:

She achieved the impossible (task of...).

The deceased (person) is survived by his wife.

He's only trying to help the rich. (metonymy)

The poor hope to live a better life. (metonymy)

If you're interested, here's futher reading you can do about using adjectives as nouns.

In addition, here is the Collins English Dictionary entry on impossible. It includes "the impossible" under its first definition of impossible as an adjective.